y' = (2y-x)/(2x-y) 微分方程?

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y' = (2y-x)/(2x-y) 微分方程?
y' = (2y-x)/(2x-y) 微分方程?

y' = (2y-x)/(2x-y) 微分方程?
dy/dx=(2y-x)/(2x-y)
dy/dx=(2y/x-1)/(2-y/x)
令y/x=u,则
u+xu'=(2u-1)/(2-u)
[(2-u)/(u²-1)]du=dx/x
两边积分得∫[(2-u)/(u²-1)]du=∫dx/x
1/2∫[1/(u-1)-3/(u+1)]du=lnx
1/2[ln(u-1)-3ln(u+1)]=lnx+C1
y/x-1=Cx²(y/x+1)³

x-y/x-x+y/y-(x+y)(x-y)/y² y/x=2 y+y'-2y=2x 微分方程y - 2y' + y = x 化简y(x+y)+(x+y)(x-y)-x^2 填空：x-y/x+y=( )/x^2-y^2 （x-y)2•(y-x)³(x-y)=? (x-y) (x-2y)+(x+2y) (x-3y)-2(x-3y) (x-4y)= (x+y)(x-y)+(x-y)平方-(x-y)(3x-y) 其中x=-2 y=3分之一已知x-y/x+y=3,求代数式5(x-y)/x+y-x+y/2(x-y) 【2(x-y)(x-y)(x-y)-8(x-y)(x-y)(x+y)+6y(x-y)(x-y)]/2(x-y)(x-y) (x+y)(x-y)-(x-y)^2如题 (x+y)(x-y)-(x-y)^2 (x-4y)(2x+y)= (x+y)(2x-3y)=? x+y>=2,x-y x+y>=2,x-y y'-2y=(e^x)-x y'+2y/x=x通解 dy/dx=(2x*x*x*y-y*y*y*y)/(x*x*x*x-2x*y*y*y)